The Apple way

Investigating on the view hierarchy shows that Apple is using UIKit and UIVisualEffectViewfor this reason. You can define a VisualEffectView with just 5 lines of code:

struct VisualEffectView: UIViewRepresentable {
    var effect: UIVisualEffect?
    func makeUIView(context: UIViewRepresentableContext<Self>) -> UIVisualEffectView { UIVisualEffectView() }
    func updateUIView(_ uiView: UIVisualEffectView, context: UIViewRepresentableContext<Self>) { uiView.effect = effect }
}

Usage Example:

struct ContentView: View {

    var body: some View {
        ZStack {
            Image("BG")
                .resizable()
                .scaledToFill()
                .edgesIgnoringSafeArea(.all)
            
            VisualEffectView(effect: UIBlurEffect(style: .dark))
                .edgesIgnoringSafeArea(.all)
                
            Text("Hello \nVisual Effect View")
                .font(.largeTitle)
                .fontWeight(.black)
                .foregroundColor(.white)
        }
    }
}

The Native SwiftUI way:

You can add .blur() modifier on anything you need to be blurry like:

struct ContentView: View {

    var body: some View {
        ZStack {
            Image("BG")
                .resizable()
                .scaledToFill()
                .edgesIgnoringSafeArea(.all)
                .blur(radius: 20) // <- this is the important modifier. The rest is just for demo
                
            Text("Hello \nSwiftUI Blur Effect")
                .font(.largeTitle)
                .fontWeight(.black)
                .foregroundColor(.white)
        }
    }
}

_{Note the top and bottom of the view}

Note that you can Group multiple views and blur them together.

iOS 15 – Apple Material

You can use iOS predefined materials with one line code:

.background(.ultraThinMaterial)